MCQs Key Class 11 maths paper 2026 1st annual paper 2026 New Book Paper Federal Board 1st Aannual

Hinzugefügt: 2026-05-15

[00:00:03]Dear Student Assalam Walekum and Welcome to my YouTube channel. D.A Students, in today's lecture, your first and 2026 mathematics paper has been discussed.

[00:00:11]I am sharing the key of its MCQs so that it can help you to know how many of your MCQs are correct. Now see, its first MCQ is very easy.

[00:00:19]First MCQ of this is that using product to sum and difference formula sin 60 sin 30 we have to find its value using sum and difference formula.

[00:00:29]sin 60 and our sin 60 and sin 30. See, we can also use the formula.

[00:00:37]Well, you might remember that sin 60, the value of sin 60 is square 3/2. Okay, right? And then sin 30 is what you get, 1 2, okay?

[00:00:48]See, when you simplify this, what will come to you? Square 3 will come up and come down 2 * 2 = 4. You are not required to use formula. Now you can see it directly from this, you can do it like this.

[00:01:00]Okay, right? And by the way, you might remember that if you want to apply the formula sinα sin beta, you have -1 cosα + beta and - cos apha - beta, meaning that when you use the formula here, it will come out to be -1 2 and cos apha + beta, okay? Alpha alpha, see if you have 60 and beta 30 then this will come cos 90.

[00:01:30]Ok? And then - cos apha - beta, so see this cos i.e. alpha you have is 60 and beta is 30. When you apply this formula 60 - 30, you will get cos 30. Ok? I am getting this solved for you from Phule also.

[00:01:46]Now look, this will come out to be -12 cos 90 is 0 and cos 30 is squared 3/2, okay? So this minus square 3/2 if this minus minus becomes plus this square will become 3/4. This means that your option B is the correct answer. So you will correct this option B.

[00:02:06]Ok?

[00:02:09]Now let's come to the part number, its part number is two. The period of tan π / 7 is now you'll remember that if you know how it's written.

[00:02:18]Ok? Tangent tangent a be x. Okay, right? And you'll remember its period was π / π / a. Ok? Look here, it's π / x. Basically it is π / x.

[00:02:34]Now look at the period because the original period of tan was π. So this is π / a. Now look here, you will get this.

[00:02:43]See, Pi will come and see here you have it 5/7, when you divide it by 5/7 then it will become reciprocal 7 π 5, this means that your option 7π / 5, this option D is the correct answer, so you will write its correct answer in this option D.

[00:03:07]Ok? Now see its part number is question number its three. A function function is periodic if Now do you remember when a function was periodic? When the function fx + p = f x. Ok? Now what has he given here that instead of p he has given t here.

[00:03:30]Ok? So ft = fx, this means that your option A is the correct answer, option A will come. Ok? This is option A A.

[00:03:47]Now let's come to question number four. Now look at question number four, he has given that the range of a + b sin 2 theta. Now you will remember that the range of sin was -1 < sin, like here 2 theta 2 thetas < 1.

[00:04:03]Now see here, first you need b, so you will multiply it by b - b < b sin 2 theta, okay and less < b will come and then see here also you have to add a.

[00:04:18]Now we will add a on both sides. Ok? a + b < equal to see here it is minus a - b < equal to see here also you will get a + b sin 2θ and less < = a + b you will get. Ok?

[00:04:42]Here it was b earlier.

[00:04:45]So see, it will come to you here also, then it will come to you a + b. See what it means, you will get a and because here there is a - b and a + b and here b is plus minus, so this will come to you, the period here i.e. the range that will come to you will be a + - b. Ok? So this is your correct option. This means that the correct option here is option B.

[00:05:17]This option B is the correct answer. Now let's come to its part number five. Now look at part number five, it is given that the number of ways of arrangement of the letters word Sunday.

[00:05:28]Now look at what you have on Sunday, look at what is the total number of letters you have on Sunday? Look at Sunday, SUN DAY, the total word is six, so you will remember that if you take out its parameter, then now see, this n parameter r will come to you 6 parameter 6 and then see, if we write this, you will get n parameter n - r, okay, so see, this will come to you 6 - 6, this will come to you 6 0, so it becomes 1. This will come to you as 6dial and the 6dial is yours 720 and by the way, see this directly, you can also remember that we can do as many factorials as you have these letters.

[00:06:22]Look, like look here, because you have six letters, we can also do direct 6orial. Ok?

[00:06:28]Its option will come to you, the option will come to you A 720, now let the question number come, you have six number of ways to select eight players from 12 R, now we will apply the combination formula here. Ok? Now look, we have a total of 12 players. From this we have to select 8. Ok? So now when we write this 12 by 12 - 8 * 8, okay and we will write this 12 * by, see we will write 12 * 11, we will also calculate it from the calculator, multiply by 10 * 9 * 8 and see here 12 - 8 will come, 4 * 3 * 2 * 1 of 4 ordinal 4 and this 8 ordinal will now get cancelled by 8 ordinal, this 4 * 3 = 12, okay this has got cancelled and then see 2 * 5 10, so this will come to you 11 5 45 and see 45, when you multiply it by 9, then this will come to you 49 495, okay so 495, so this option which is 495 option B is the correct answer.

[00:07:55]Now let's come to question number seven.

[00:07:58]Look in question number seven, it is written that factorize z², right? You need to factorize z² + 289.

[00:08:08]So here we will apply complex number.

[00:08:10]See 289. We'll write this as z², and look, we'll write it as -iot² because iot² gives you -1.

[00:08:21]Again this minus plus 1 becomes 289 and then see this becomes z² and 289 is the square of 17. Ok?

[00:08:31]So we will put the square of 17iot here.

[00:08:34]Now we will apply the formula here.

[00:08:36]a + b a - b so this will come z + 17iot * z - 17iot so this is your option, see the option z + 17 z - 17iota so this is your option D is the correct answer so this option D will come to you.

[00:08:57]Ok?

[00:09:00]z + 17 z - 17iot Now let's look at part number nine. Now the rank of sorry part number at rent of matrix is ​​rent rank of matrix you know rank is you have number of non rank is equal to number of non zero rows when we convert it into H1 form.

[00:09:32]Ok? Now look here, you have this, look you have zero and what is the number of non- zero rows? There is two. Ok? So this will come to you, its answer will come to you.

[00:09:44]So this two is the correct answer.

[00:09:47]Now let's look at question number nine.

[00:09:49]Look at question number nine, it is given that a consistent system must have at least one consistent system. Now you will remember when the system is consistent?

[00:10:00]What is its solution? There should be at least one solution. What's up? At least one solution.

[00:10:06]So this option B is the correct answer.

[00:10:11]Ok? So this is your correct answer APS One Solution.

[00:10:18]Now look at the next part, the nth term of n AP is, so you remember that the nth term an = this is a + n - 1 * d. Now look at the option here, option C is a + n - 1 * d, okay? Then look what you have next is the argument of z = 3 + ioty argument. You remember that θ = tangent inverse y over x, right?

[00:10:52]So θ = tg inverse y, which is the quotient of our imaginary number, this is one, and x squared here is 3, and tan inverse 1 is 3, so you have π/6 = 30.

[00:11:11]Ok? 30° So see which option do you have? π/6 is option A.

[00:11:21]Now look ahead, the next question you have is question number 12. Now look at question 12, it is given that HP decreases when.

[00:11:27]Now see HP see when does the decree happen? When i.e. what is AP? There should be an increase.

[00:11:33]Look, you must remember that HP is the inverse of AP. Now see, in AP you have it, for example, 1 2 3 4 5. So see HP is its reciprocal. Ok? So 1 will become 1/2 1/3 1/4 so see what happens?

[00:11:55]Decrease happens. Ok? So this will be a decree. So this option B is the correct answer.

[00:12:01]Now let's come to question number 13.

[00:12:04]In question number 13 it is given that binomial expansion is used. Now you will remember that we use this binomial expansion, this Pascal triangle.

[00:12:13]Ok? This is your Pascal's triangle. Option A is the correct answer. Now let's come to question number 14. Now in question number 14 see that in mathematical induction assume true for n. Ok? True for we suppose here when do n equal to? In the result, in the base case, in the proof and in the hypothesis. So in the base case, you will remember. We used to read that we take n = 1. Okay, right? Now in the hypothesis i.e. we took n = k.

[00:12:44]That is, we used to suppose that if this is true for n = n then it will obviously be true for n = k also. So this option D is the correct answer.

[00:12:54]Now let's look at question number 15.

[00:12:57]Question number 15 is that in polynomial division the degree of reminder is now see whenever you divide a polynomial by something then what will be the degree of reminder always? Very few will come. Okay, right? So what will the degree always bring? The lace will come. Okay, right?

[00:13:15]Less than divisor.

[00:13:20]So this option D is the correct answer. Ok?

[00:13:25]Okay, now look at the next part, question number 16, which is if x - 2 is a factor of fx then f2. So just look at when because this is a factor. Okay, right? So look at fx, because you have the factor x - 2, so when you put f2 here, 2 - 2 will obviously satisfy it, when it is factored, it comes back to you as zero. Ok? So what will your f2 be? Zero will come. So this option is correct.

[00:13:54]Now coming to question number 17, the scalar product of two non-zero vectors is maximum when both vectors are R. Now you might remember that in the dot product, you have a.b = ab cos theta, okay? ab cos theta ab cos theta okay?

[00:14:17]Now let's take ab cos theta, so when we look at this, when we look at the maximum, when θ is 0, what is cos 0? Do you remember what We Know That Cos 0 is? There is a forest. Okay, right? So if cos 0 is 1 then what will you get that you will get the maximum result. Ok? When perpendicular, theta becomes 90 and then 0.

[00:14:38]This means what will the vectors be? Will be parallel.

[00:14:43]Now let's come to question number 18. Now given two vectors. The vector u gives you 2i + 3 or -4k and the vector v gives you -2i - k so then the dot product and you remember the dot product when you look at u. Will remove u.

[00:15:01]Look at this you remember that i.

[00:15:04]J.j and k.k is 1. All the rest are zero.

[00:15:09]But when you add 2 * 2 here, it will come to you -4. Okay, right? So when we remove the u dot, see, it will come to -4, the rest will be 0 and then when we do k, then minus minus plus and 4, the coefficient of k is -4 whereas here the coefficient of k is -1, so see, this will come to you +4, see, this will come to you 0, this means that the option of this will come to you zero, okay, it has come to you zero, this option D is the correct answer. Now look at the second last one, the vectors P, the vectors P, Q and R are coplanar if.

[00:15:56]So now you remember what happens in this, your vector is your scalar triple.